Two girls went shopping. In the first shop, they spent half of what they had…
2023
Two girls went shopping. In the first shop, they spent half of what they had in their purse plus 2 rupees. In the next shop, they spent half of the remaining amount plus 5 rupees. In the next shop, they spent half of what remained. The remaining 5 rupees was spent on coffee. How much money did they start with?
- A.
64
- B.
56
- C.
60
- D.
52
Show answer & explanation
Correct answer: A
A multi-stage "spend half of what remains, plus a fixed extra amount" word problem is solved by translating each stage into an equation: if an amount v remains before a stage, and that stage spends v/2 plus a fixed amount c, then what is left after that stage is v/2 minus c. Chaining these stage-by-stage equations from the starting amount down to the final known remainder gives one equation in the single unknown, which can then be solved directly.
Let the amount they started with be x rupees.
In the first shop they spend x/2 + 2, so the amount remaining is x − (x/2 + 2) = x/2 − 2.
In the second shop they spend half of that remaining amount plus 5 rupees, so what is left is (x/2 − 2)/2 − 5 = x/4 − 6.
In the third shop they spend half of what remained, with no extra fixed amount this time, leaving (x/4 − 6)/2 = x/8 − 3.
This final remaining amount is exactly the 5 rupees spent on coffee, so x/8 − 3 = 5.
Solving: x/8 = 8, so x = 64.
Cross-check by substituting x = 64 through all three stages: the first shop leaves 64/2 − 2 = 30; the second shop leaves 30/2 − 5 = 10; the third shop leaves 10/2 = 5 — exactly the 5 rupees spent on coffee, confirming 64 is correct.